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Discrete Structures
(COT 3100) Final Exam
Spring 2000
Section 2
4/25/00
Lecturer: Arup Guha
TA: __________________
First Name : ________________
Last Name : ________________
(Note: On all questions that contain a blank line, please place your answer on that
line clearly. If a short answer question doesn’t have a line for you to place your
answer, please neatly write your answer directly below the question. Circle TRUE
or FALSE for all true/false questions.)
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for leaving the question blank, and negative one point for an incorrect response.
a)
(p
⇒
q)
⇔
(
¬
q
⇒
¬
p)
TRUE
b)
5
x
2200
y [x + y = 10]
FALSE
c)
If the contrapositive of a statement is true,
FALSE
then the converse of statement is true as well.
d)
¬
[
2200
x p(x)]
⇔
5
x
¬
p(x)
TRUE
e)
Let A, B and C be sets.
If A
⊆
B and A
∩
B = B
∩
C, then A = C.
FALSE
f)
The total number of subsets of {2,4,5,6,9} is 25.
FALSE
g)
If a  b and a  c, then gcd(b,c)
≥
a.
TRUE
h)
If R is a bijection (A
→
B), and S is a surjection
(B
→
C), then R
°
S is an injection (A
→
C).
FALSE
i)
Let A and B be sets of strings such that A*
⊆
B*,
then A
⊆
B.
FALSE
j)
The number of bijective functions
over a set A={1,2,3} is 6.
TRUE
k)
A DFA must have more than one final state.
FALSE
l)
A language containing a finite number of
strings is a regular language.
TRUE
m)
A DFA with n states that accepts at least one
string MUST accept at least one string with
a length less than or equal to n.
TRUE
n)
a+ is NOT a valid regular expression.
TRUE
o)

λ
 = 0.
TRUE
2) (8 pts) Fill in the following Truth Table
to evaluate the expression (p
∧
(q
∨
¬
r))
∨
(r
∧
¬
q).
p
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 Fall '09

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